Always good to follow the instructions
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But I would bet that the keep-it-on recommendation refers to the after-burnin phase and *not* the initial burn-in itself. If you are just keeping the DAC on without signal, you are simply keeping it warm, not burnin it in. That keep-it-on advice is usually related to the fact that sensitive clocks need a few minutes/hours to warm-up/stabilize after a cold start .. tubes too .. caps maybe .. etc.
You could read lots about burnin for all sorts of components over the net .. it's *always* done with full signal through ... some go as far as building special burnin playlists with various types of music and one can buy special burnin cd-s or special cable burnin machines.
Someone please correct me if I'm wrong, but I doubt the Iggy is any different ... OTOH, never heard of days-long warmups either so there may be something to the Iggy .. but I seriously doubt that in the burnin case.
Long story short: you cannot truly burn-in an audio component without a signal, same as you cannot burn (almost) anything without a fire